Quantum fields on manifolds: PCT and gravitationally induced thermal states
Jul, 198224 pages
Published in:
- Annals Phys. 141 (1982) 201-224
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Abstract: (Elsevier)
We formulate an axiomatic scheme, designed to provide a framework for a general, rigorous theory of relativistic quantum fields on a class of manifolds, that includes Kruskal's extension of Schwarzschild space-time, as well as Minkowski space-time. The scheme is an adaptation of Wightman's to this class of manifolds. We infer from it that, given an arbitrary field (in general, interacting) on a manifold X , the restriction of the field to a certain open submanifold X (+) , whose boundaries are event horizons, satisfies the Kubo-Martin-Schwinger (KMS) thermal equilibrium conditions. This amounts to a rigorous, model-independent proof of a generalised Hawking-Unruh effect. Further, in cases where the field enjoys a certain PCT symmetry, the conjugation governing the KMS condition is just the PCT operator. The key to these results is an analogue, that we prove, of the Bisognano-Wichmann theorem. [ J. Math. Phys. 17 (1976), Theorem 1]. We also construct an alternative scheme by replacing a regularity condition at an event horizon by the assumption that the field in X (+) is in a ground, rather than a thermal, state. We show that, in this case, the observables in X (+) are uncorrelated to those in its causal complement, X (−) , and thus that the event horizons act as physical barriers. Finally, we argue that the choice between the two schemes must be dictated by the prevailing conditions governing the state of the field.References(33)
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